© Oxford University; the media items are released with a Creative Commons licence
http://creativecommons.org/licenses/byncsa/2.0/uk/
Nick Trefethen FRS, Professor of Numerical Analysis at Oxford University, teaches a course for DPhil (PhD) students across all the science departments at the university. The course is distinctive for its exceptionally strong conceptual basis, focussing on fundamental ideas of numerical algorithms and the world of science and engineering they sustain. Historical and philosophical notes on many subjects make these lectures unusual, offering deeper understanding and new perspectives for anyone involved with numerical analysis or scientific computing.
en
Tue, 06 Dec 2022 09:20:27 +0000
https://www.maths.ox.ac.uk/
Scientific Computing for DPhil Students
Oxford University
Oxford University
podcasts@it.ox.ac.uk
no
http://mediapub.it.ox.ac.uk/sites/fred/files/images/albumcovers/scientificcomputingdphilstudents.jpg
Scientific Computing for DPhil Students
https://www.maths.ox.ac.uk/

1
scientific computing
numerical analysis
linear algebra
optimization
In this lecture, Professor Trefethen first provides an overview of the field of linear algebra and optimization. Secondly, he discusses the question of how fast we can solve Ax=3Db? Thirdly, he discusses sparse matrices
http://rss.oucs.ox.ac.uk/tag:20221206:090828:000:file:297277:video
http://media.podcasts.ox.ac.uk/maths/scicomp/20151013MT_scientific_computing_lecture_01.mp4
In this lecture, Professor Trefethen first provides an overview of the field of linear algebra and optimization. Secondly, he discusses the question of how fast we can solve Ax=3Db? Thirdly, he discusses sparse matrices
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this lecture, Professor Trefethen first provides an overview of the field of linear algebra and optimization. Secondly, he discusses the question of how fast we can solve Ax=3Db? Thirdly, he discusses sparse matrices Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization
Nick Trefethen
3032
Mon, 03 Oct 2016 16:15:00 +0100

2
scientific computing
numerical analysis
linear algebra
optimization
In this lecture, Professor Trefethen discusses the topic of conjugate gradients and the convergence of CG.
http://rss.oucs.ox.ac.uk/tag:20221206:090900:000:file:297278:video
http://media.podcasts.ox.ac.uk/maths/scicomp/20151015MT_scientific_computing_lecture_02.mp4
In this lecture, Professor Trefethen discusses the topic of conjugate gradients and the convergence of CG.
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this lecture, Professor Trefethen discusses the topic of conjugate gradients and the convergence of CG. Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization
Nick Trefethen
3180
Mon, 03 Oct 2016 16:28:29 +0100

3
scientific computing
numerical analysis
linear algebra
optimization
In this lecture, Professor Trefethen discusses preconditioned CG and also provides examples of preconditioners
http://rss.oucs.ox.ac.uk/tag:20221206:090928:000:file:297275:video
https://media.podcasts.ox.ac.uk/maths/scicomp/20151027MT_scientific_computing_lecture_03.mp4
In this lecture, Professor Trefethen discusses preconditioned CG and also provides examples of preconditioners
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this lecture, Professor Trefethen discusses preconditioned CG and also provides examples of preconditioners Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization
Nick Trefethen
3279
Mon, 03 Oct 2016 16:30:47 +0100

4
scientific computing
numerical analysis
linear algebra
optimization
In this lecture, Professor Trefethon provides a definition of numerical analysis and provides an overview of matrix iterations, including a discussion on the Lanczos iteration. He also reviews various numerical software tools and information sources.
http://rss.oucs.ox.ac.uk/tag:20221206:090956:000:file:297276:video
http://media.podcasts.ox.ac.uk/maths/scicomp/20151030MT_scientific_computing_lecture_04.mp4
In this lecture, Professor Trefethon provides a definition of numerical analysis and provides an overview of matrix iterations, including a discussion on the Lanczos iteration. He also reviews various numerical software tools and information sources.
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this lecture, Professor Trefethon provides a definition of numerical analysis and provides an overview of matrix iterations, including a discussion on the Lanczos iteration. He also reviews various numerical software tools and information sources. Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization
Nick Trefethen
2901
Mon, 03 Oct 2016 16:32:58 +0100

5
scientific computing
numerical analysis
linear algebra
optimization
In this lecture, Professor Trefethen discusses matrices, vectors and expansions, including orthogonal vectors and matrices.
http://rss.oucs.ox.ac.uk/tag:20221206:091026:000:file:297279:video
http://media.podcasts.ox.ac.uk/maths/scicomp/20151103MT_scientific_computing_lecture_05.mp4
In this lecture, Professor Trefethen discusses matrices, vectors and expansions, including orthogonal vectors and matrices.
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this lecture, Professor Trefethen discusses matrices, vectors and expansions, including orthogonal vectors and matrices. Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization
Nick Trefethen
3168
Mon, 03 Oct 2016 16:35:02 +0100

6
scientific computing
numerical analysis
linear algebra
optimization
In this lecture, Professor Trefethen discusses QR factorization, the computation of the QR factorization, and linear leastsquares.
http://rss.oucs.ox.ac.uk/tag:20221206:091053:000:file:297280:video
http://media.podcasts.ox.ac.uk/maths/scicomp/20151106MT_scientific_computing_lecture_06.mp4
In this lecture, Professor Trefethen discusses QR factorization, the computation of the QR factorization, and linear leastsquares.
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this lecture, Professor Trefethen discusses QR factorization, the computation of the QR factorization, and linear leastsquares. Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization
Nick Trefethen
2978
Mon, 03 Oct 2016 16:36:10 +0100

7
scientific computing
numerical analysis
linear algebra
optimization
In this lecture, Professor Trefethen discusses floating point arithmetic and backward error analysis.
http://rss.oucs.ox.ac.uk/tag:20221206:091118:000:file:297297:video
http://media.podcasts.ox.ac.uk/maths/scicomp/20151110MT_scientific_computing_lecture_07.mp4
In this lecture, Professor Trefethen discusses floating point arithmetic and backward error analysis.
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this lecture, Professor Trefethen discusses floating point arithmetic and backward error analysis. Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization
Nick Trefethen
3221
Mon, 03 Oct 2016 16:39:35 +0100

8
scientific computing
numerical analysis
linear algebra
optimization
In this lecture, Professor Trefethen discusses matrix factorizations and SVD.
http://rss.oucs.ox.ac.uk/tag:20221206:091147:000:file:297298:video
http://media.podcasts.ox.ac.uk/maths/scicomp/20151113MT_scientific_computing_lecture_08.mp4
In this lecture, Professor Trefethen discusses matrix factorizations and SVD.
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this lecture, Professor Trefethen discusses matrix factorizations and SVD. Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization
Nick Trefethen
3084
Mon, 03 Oct 2016 16:40:51 +0100

9
scientific computing
numerical analysis
linear algebra
optimization
In this lecture, Professor Trefethen provides a demonstration of Chebfun.
http://rss.oucs.ox.ac.uk/tag:20221206:091218:000:file:297299:video
http://media.podcasts.ox.ac.uk/maths/scicomp/20151117MT_scientific_computing_lecture_09.mp4
In this lecture, Professor Trefethen provides a demonstration of Chebfun.
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this lecture, Professor Trefethen provides a demonstration of Chebfun. Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization
Nick Trefethen
2921
Mon, 03 Oct 2016 16:41:54 +0100

10
scientific computing
numerical analysis
linear algebra
optimization
In this lecture, Professor Trefethen discusses Newton's methods for 1) a single equation, 2) a system of equations, and 3) minimizing a function of 1 variable.
http://rss.oucs.ox.ac.uk/tag:20221206:091253:000:file:297368:video
http://media.podcasts.ox.ac.uk/maths/scicomp/20151120MT_scientific_computing_lecture_10.mp4
In this lecture, Professor Trefethen discusses Newton's methods for 1) a single equation, 2) a system of equations, and 3) minimizing a function of 1 variable.
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this lecture, Professor Trefethen discusses Newton's methods for 1) a single equation, 2) a system of equations, and 3) minimizing a function of 1 variable. Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization
Nick Trefethen
2966
Mon, 03 Oct 2016 16:44:35 +0100

11
scientific computing
numerical analysis
linear algebra
optimization
In this lecture, Professor Trefethen discusses Newton's methods for minimizing a function of several variables. He then moves on from Newton's method to practical optimization.
http://rss.oucs.ox.ac.uk/tag:20221206:091325:000:file:297369:video
http://media.podcasts.ox.ac.uk/maths/scicomp/20151124MT_scientific_computing_lecture_11.mp4
In this lecture, Professor Trefethen discusses Newton's methods for minimizing a function of several variables. He then moves on from Newton's method to practical optimization.
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this lecture, Professor Trefethen discusses Newton's methods for minimizing a function of several variables. He then moves on from Newton's method to practical optimization. Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization
Nick Trefethen
2982
Mon, 03 Oct 2016 16:46:23 +0100

12
scientific computing
numerical analysis
linear algebra
optimization
In this lecture, Professor Trefethen discusses NEOS and COINOR, constraints and linear programming, and quadratic programming and linear constraints.
http://rss.oucs.ox.ac.uk/tag:20221206:091353:000:file:297383:video
http://media.podcasts.ox.ac.uk/maths/scicomp/20151127MT_scientific_computing_lecture_12.mp4
In this lecture, Professor Trefethen discusses NEOS and COINOR, constraints and linear programming, and quadratic programming and linear constraints.
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this lecture, Professor Trefethen discusses NEOS and COINOR, constraints and linear programming, and quadratic programming and linear constraints. Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization
Nick Trefethen
3023
Mon, 03 Oct 2016 16:47:42 +0100

13
scientific computing
numerical analysis
linear algebra
optimization
nonlinear dynamics
In this lecture, Professor Trefethen discusses ODEs and IVPs, RungeKutta and multistep formulas, IVP codes in MATLAB and Simulink, and in the end reviews IVP solutions in Chebfun.
http://rss.oucs.ox.ac.uk/tag:20221206:091420:000:file:297659:video
http://media.podcasts.ox.ac.uk/maths/scicomp/20160122HT_scientific_computing_lecture_01.mp4
In this lecture, Professor Trefethen discusses ODEs and IVPs, RungeKutta and multistep formulas, IVP codes in MATLAB and Simulink, and in the end reviews IVP solutions in Chebfun.
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this lecture, Professor Trefethen discusses ODEs and IVPs, RungeKutta and multistep formulas, IVP codes in MATLAB and Simulink, and in the end reviews IVP solutions in Chebfun. Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization,nonlinear dynamics
Nick Trefethen
3183
Mon, 17 Oct 2016 12:35:58 +0100

14
scientific computing
numerical analysis
linear algebra
optimization
nonlinear dynamics
In this lecture, Professor Trefethen discusses order of accuracy, convergence and stability, and adaptive ODE codes.
http://rss.oucs.ox.ac.uk/tag:20221206:091544:000:file:297602:video
http://media.podcasts.ox.ac.uk/maths/scicomp/20160122HT_scientific_computing_lecture_02.mp4
In this lecture, Professor Trefethen discusses order of accuracy, convergence and stability, and adaptive ODE codes.
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this lecture, Professor Trefethen discusses order of accuracy, convergence and stability, and adaptive ODE codes. Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization,nonlinear dynamics
Nick Trefethen
2981
Mon, 17 Oct 2016 12:41:34 +0100

15
scientific computing
numerical analysis
linear algebra
optimization
nonlinear dynamics
In this lecture, Professor Trefethen discusses planetary motions, chaos and Lyapunov exponents, the Lorenz equations, and lastly Sinai billiards and the SIAM 100digit challenge.
http://rss.oucs.ox.ac.uk/tag:20221206:091609:000:file:306127:video
http://media.podcasts.ox.ac.uk/maths/scicomp/20190122HTscientific_computing_lecture_15_replacement720p.mp4
In this lecture, Professor Trefethen discusses planetary motions, chaos and Lyapunov exponents, the Lorenz equations, and lastly Sinai billiards and the SIAM 100digit challenge.
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this lecture, Professor Trefethen discusses planetary motions, chaos and Lyapunov exponents, the Lorenz equations, and lastly Sinai billiards and the SIAM 100digit challenge. Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization,nonlinear dynamics
Nick Trefethen
3045
Mon, 17 Oct 2016 12:43:37 +0100

16
scientific computing
numerical analysis
linear algebra
optimization
nonlinear dynamics
In this lecture, Professor Trefethen discusses stability regions, stiffness, and looks at BVPs in Chebfun.
http://rss.oucs.ox.ac.uk/tag:20221206:091637:000:file:297604:video
http://media.podcasts.ox.ac.uk/maths/scicomp/20160129HT_scientific_computing_lecture_04.mp4
In this lecture, Professor Trefethen discusses stability regions, stiffness, and looks at BVPs in Chebfun.
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this lecture, Professor Trefethen discusses stability regions, stiffness, and looks at BVPs in Chebfun. Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization,nonlinear dynamics
Nick Trefethen
3050
Mon, 17 Oct 2016 12:44:53 +0100

17
scientific computing
numerical analysis
linear algebra
optimization
nonlinear dynamics
In this lecture, Professor Trefethen discusses PDEs in science and engineering, and explicit 1D finite differences.
http://rss.oucs.ox.ac.uk/tag:20221206:091708:000:file:297605:video
http://media.podcasts.ox.ac.uk/maths/scicomp/20160202HT_scientific_computing_lecture_05.mp4
In this lecture, Professor Trefethen discusses PDEs in science and engineering, and explicit 1D finite differences.
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this lecture, Professor Trefethen discusses PDEs in science and engineering, and explicit 1D finite differences. Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization,nonlinear dynamics
Nick Trefethen
3078
Mon, 17 Oct 2016 12:46:31 +0100

18
scientific computing
numerical analysis
linear algebra
optimization
nonlinear dynamics
In this lecture, Professor Trefethen discusses numerical instability and implicit 1D finite differences.
http://rss.oucs.ox.ac.uk/tag:20221206:091738:000:file:297606:video
http://media.podcasts.ox.ac.uk/maths/scicomp/20160205HT_scientific_computing_lecture_06.mp4
In this lecture, Professor Trefethen discusses numerical instability and implicit 1D finite differences.
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this lecture, Professor Trefethen discusses numerical instability and implicit 1D finite differences. Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization,nonlinear dynamics
Nick Trefethen
2959
Mon, 17 Oct 2016 12:47:38 +0100

19
scientific computing
numerical analysis
linear algebra
optimization
nonlinear dynamics
In this lecture, Professor Trefethen discusses order of accuracy and reactiondiffusion equations and other stiff PDEs.
http://rss.oucs.ox.ac.uk/tag:20221206:091809:000:file:297607:video
http://media.podcasts.ox.ac.uk/maths/scicomp/20160209HT_scientific_computing_lecture_07.mp4
In this lecture, Professor Trefethen discusses order of accuracy and reactiondiffusion equations and other stiff PDEs.
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this lecture, Professor Trefethen discusses order of accuracy and reactiondiffusion equations and other stiff PDEs. Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization,nonlinear dynamics
Nick Trefethen
3128
Mon, 17 Oct 2016 12:48:38 +0100

20
scientific computing
numerical analysis
linear algebra
optimization
nonlinear dynamics
In this lecture, Professor Trefethen discusses finite differencing in general grids and multiple space dimensions.
http://rss.oucs.ox.ac.uk/tag:20221206:091835:000:file:297608:video
http://media.podcasts.ox.ac.uk/maths/scicomp/20160212HT_scientific_computing_lecture_08.mp4
In this lecture, Professor Trefethen discusses finite differencing in general grids and multiple space dimensions.
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this lecture, Professor Trefethen discusses finite differencing in general grids and multiple space dimensions. Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization,nonlinear dynamics
Nick Trefethen
3070
Mon, 17 Oct 2016 12:49:37 +0100

21
scientific computing
numerical analysis
linear algebra
optimization
nonlinear dynamics
In this lecture, Professor Trefethen discusses Fourier spectral discretization and Fourier spectral discretization via FFT.
http://rss.oucs.ox.ac.uk/tag:20221206:091904:000:file:297612:video
http://media.podcasts.ox.ac.uk/maths/scicomp/20160216HT_scientific_computing_lecture_09.mp4
In this lecture, Professor Trefethen discusses Fourier spectral discretization and Fourier spectral discretization via FFT.
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this lecture, Professor Trefethen discusses Fourier spectral discretization and Fourier spectral discretization via FFT. Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization,nonlinear dynamics
Nick Trefethen
3002
Mon, 17 Oct 2016 12:50:54 +0100

22
scientific computing
numerical analysis
linear algebra
optimization
nonlinear dynamics
In this lecture, Professor Trefethen discusses Fourier, Laurent, and Chebyshev. Then, Chebyshev series and interpolants
http://rss.oucs.ox.ac.uk/tag:20221206:091930:000:file:297609:video
http://media.podcasts.ox.ac.uk/maths/scicomp/20160219HT_scientific_computing_lecture_10.mp4
In this lecture, Professor Trefethen discusses Fourier, Laurent, and Chebyshev. Then, Chebyshev series and interpolants
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this lecture, Professor Trefethen discusses Fourier, Laurent, and Chebyshev. Then, Chebyshev series and interpolants Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization,nonlinear dynamics
Nick Trefethen
3050
Mon, 17 Oct 2016 12:52:25 +0100

23
scientific computing
numerical analysis
linear algebra
optimization
nonlinear dynamics
In this lecture, Professor Trefethen discusses Chebyshev spectral discretization.
http://rss.oucs.ox.ac.uk/tag:20221206:091957:000:file:297610:video
http://media.podcasts.ox.ac.uk/maths/scicomp/20160223HT_scientific_computing_lecture_11.mp4
In this lecture, Professor Trefethen discusses Chebyshev spectral discretization.
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this lecture, Professor Trefethen discusses Chebyshev spectral discretization. Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization,nonlinear dynamics
Nick Trefethen
3050
Mon, 17 Oct 2016 12:53:10 +0100

24
scientific computing
numerical analysis
linear algebra
optimization
nonlinear dynamics
In this concluding lecture, Professor Nick Trefethen discusses the question Who invented the great numerical algorithms?
http://rss.oucs.ox.ac.uk/tag:20221206:092027:000:file:297611:video
http://media.podcasts.ox.ac.uk/maths/scicomp/20160226HT_scientific_computing_lecture_12.mp4
In this concluding lecture, Professor Nick Trefethen discusses the question Who invented the great numerical algorithms?
http://creativecommons.org/licenses/byncsa/2.0/uk/
In this concluding lecture, Professor Nick Trefethen discusses the question Who invented the great numerical algorithms? Creative Commons AttributionNonCommercialShare Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/byncsa/2.0/uk/
scientific computing,numerical analysis,linear algebra,optimization,nonlinear dynamics
Nick Trefethen
3212
Mon, 17 Oct 2016 12:54:14 +0100